Irrational Number and Solving Equation.

[lvl107]

Hello everyone,

I have a question and wish learning. It's about "Irrational Number and Solving Equation".

Thanks in advance.

Regards,

Loi,

[RichardJ]

Your equation requires that the decimal part of sqrt(x) be equal to the expression on the right hand side. However, since there is nothing to specify what the integer part of sqrt(x) has to be, your equation has an infinite number of possible solutions.

[lvl107]

Thanks for your suggestion, Richard.

Following up the suggestion, above. Checking with x=6; x=7; x=8. We have:

So x=7 is the one of the solutions. And the rests of the solutions are the question.

Thanks in advance.

Regards,

Loi.

[RichardJ · Accepted solution]

sqrt(x)-floor(sqrt(x)) is the non-integer part of sqrt(x). You know that is equal to the right hand side, or to sqrt(7)-2. So you can generate other solutions just be adding an integer to that number.

[lvl107]

I got it. Many, many thanks, Richard. And I have one more related question in "Mathcad Usage". Is there a press button, doing the following:

transpose --->

Thanks in advance.

Regards,

Loi.

[RichardJ]

No, sorry. You can go from the one on the right to the one on the left just by evaluating symbolically, but I don't think there is a way to reverse it.

[lvl107]

Thanks again, Richard.

Best regards,

Loi.

[SteenGroðe]

Just a bit more (all in version 11.2)

[lvl107]

I greatly appreciate your help, Steen. I have comprehended that as the following:

Many thanks, Steen.

Regards,

Loi.

[MikeArmstrong]

So x=7 is the one of the solutions. And the rests of the solutions are the question.

Is that you sending love to Richard????

Mike

[lvl107]

Sorry, Mike. It's a half due to my English and a half due to accidentally hit key.

Thanks for reminding me.

Regards,

Loi.